Of the 12 temporary employees in a company, 4 will be made permanent. If 5 of the 12 temporary employees are male, how many groups of temp employees can consist of 3 women and 1 man?
1)22
2) 35
3) 56
4) 70
5) 105
OA is 70[spoiler]
Thank you very much [/spoiler]
Doubt
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 GMATGuruNY
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The problem has been transcribed incorrectly.
It should indicate that 5 of the 12 temporary employees are WOMEN:
Number of ways to choose 1 man from 7 options = 7C1 = 7.
Number of ways to choose 3 women from 5 options = 5C3 = (5*4*3)/(3*2*1) = 10.
To combine the options above, we multiply:
7*10 = 70.
The correct answer is D.
It should indicate that 5 of the 12 temporary employees are WOMEN:
Since 5 of the 12 temporary employees are women, 7 are men.Of the 12 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man?
A. 22
B. 35
C. 56
D. 70
E. 105
Number of ways to choose 1 man from 7 options = 7C1 = 7.
Number of ways to choose 3 women from 5 options = 5C3 = (5*4*3)/(3*2*1) = 10.
To combine the options above, we multiply:
7*10 = 70.
The correct answer is D.
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 Brent@GMATPrepNow
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Take the task of selecting the employees and break it into stages.Of the 12 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man?
A. 22
B. 35
C. 56
D. 70
E. 105
Stage 1: Select the 3 women
The order in which we select the women does not matter, so we can use combinations.
We can select 3 women from 5 women in 5C3 ways (= 10 ways)
Aside: If anyone is interested, we have a free video on calculating combinations (like 5C3) in your head: https://www.gmatprepnow.com/module/gmatcounting?id=789
Stage 2: Select the 1 man
There are 7 men, so we can complete this stage in 7 ways.
By the Fundamental Counting Principle (FCP), we can complete the two stages (and thus select the permanent employees) in (10)(7) ways ([spoiler]= 70 ways[/spoiler])
Answer: D

Note: the FCP can be used to solve the majority of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmatcounting?id=775
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Cheers,
Brent

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 DavidG@VeritasPrep
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Check out Mitch's post (second from top.) He notes that the initial question had been transcribed incorrectly.Gurpreet singh wrote:Question stem says 5 of 12 emp are male, while the calculations have been done for female

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